Hello Mr Yanofsky,

I loved your general papper.It is one of my favorite.Because your have well generalised about maths.Noether I like also ,she was very relevant.I like the determionism and the objectivity of methods.

I liked also your interpretation of chaos and order.Especialy how you show the harmony in its generality and order by these mathema and symmetries.I like also these...

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Hello Mr Yanofsky,

I loved your general papper.It is one of my favorite.Because your have well generalised about maths.Noether I like also ,she was very relevant.I like the determionism and the objectivity of methods.

I liked also your interpretation of chaos and order.Especialy how you show the harmony in its generality and order by these mathema and symmetries.I like also these geometrical algebras, I try to formalise the 3D sphères and the spherical geom alg that I invented.The convergences with the spherical volumes could be analysed instead of points.The associativity, the commutativity or not the domains, the scalars the vectors.It is possible to find the correct universal partition of 3D sphères.The récurrences when we follow this order of numbers like you said appear with these maths like a quiet harmonical road.But there are still many convergences, the Mtheory especially to find to harmonise all thjis puzzle.They turn these 3D spherical volumes Professor Yanofsky.I see relevances so in your reasonings about the convergences between the mathematical singularities and their main codes of buildinbg if In can say and the gravitational physical codes.That becomes so very relevant there when we consider the maths and the singularities.The main primordial in 1D of Mr Witten with strings seems relevant ,but If I can the aether doe not seem to be luminiferous but gravitational.That implies an other reasoning.These spherical volumes Professor,They turn so they are .....Inside this 3D sphere.Now with the multiverse and mathematical singularities and the spherical volumes considering these singularities, that becomes very intriguing considering the real universal singularity because if a multispheres exist so we must also consider a central sphere even for this multiverse multispheres for me.That is why that becomes very very relavnt about our constants for each universe ,in logic the main central cosm singularity and its volume implies these aethers, gravitational so implying our constants like c ,G,h,alpha fine struct cst or this or that.That intrigues me a lot at this moment these volumes and these singularities if Mr Tegmark is right about the fact that we have several universes, 3d sphères for me.These sphericalgeometrical algebras with these volumes and the good operators ,vectors and scalars,domains, groups....can explain many things in our universe and others if they exist.In all case an interesting thing is that we retrun always at a main primordial singularity,cosmological even for multispheres.Dirac helps us :)

Congratulations for your papper and good luck in this contest.

Best

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Dear Noson,

glad to see you entering this contest!

I like your idea that finding (simple) mathematical laws in nature is, in part, due to a certain selection bias. Ultimately, to connect with the contest's topic, one might then speculate that it's not nature working according to mathematical laws that gives rise to goal-directed behavior, but rather, that it's the other way around:...

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Dear Noson,

glad to see you entering this contest!

I like your idea that finding (simple) mathematical laws in nature is, in part, due to a certain selection bias. Ultimately, to connect with the contest's topic, one might then speculate that it's not nature working according to mathematical laws that gives rise to goal-directed behavior, but rather, that it's the other way around: human beings, following their goals, investigate precisely those systems simple enough as to be easily mathematized, in order to further these goals (which, one may presume, include some measure of predicting the future of such mathematizable systems).

Where most would see physics as an increased specification, a sort of chipping-away process in order to get at the underlying capital-T Truth of it all, you see rather a broadening process, being forced to accept ever-more general structures into the formulation. I think that's an interesting take on the matter (and in some conceptual sense related to investigating the world not by means of uncovering some set of positive truths, but rather, by pointing out the photonegative limitations that eventually serve to define the boundaries of this set, as you do in your popular-level book).

In the end, it seems to me you come close to a formulation of 'law without law', as envisioned by Wheeler. Something like that might offer a way forward on one of the problems for your view you note: namely, that it seems that in particular, the fundamental dynamics of the world are the most exactly mathematizable. One might view this description however as merely effective, originating in some essentially chaotic underlying dynamics.

Take a process operating on a given bit string: even if bits are flipped at random, without any law at all, there are certain predictions that can be made for the gross properties of the string---such as that it will tend towards an equilibrium of roughly half as many 1s and 0s, e.g. This also eliminates the worry of 'who fixes the laws': in that sense, the laws are merely descriptive, rather than proscribing the way the universe unfolds.

Good luck with your essay!

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Dear Prof Yanofsky,

Good essay on Structures of the mathematics and number systems required for explaining this Universe or Multiverse…

Your observations like…

1. “Since we have no contact with possible other universes, the question of the existence of the multiverse is essentially metaphysics.” And “Rather than saying that the universe is very structured, say that...

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Dear Prof Yanofsky,

Good essay on Structures of the mathematics and number systems required for explaining this Universe or Multiverse…

Your observations like…

1. “Since we have no contact with possible other universes, the question of the existence of the multiverse is essentially metaphysics.” And “Rather than saying that the universe is very structured, say that the universe is chaotic and lacks structure. The reason why we see so much structure is that scientists act like a sieve and pull out only those phenomena that are predictable. They do not take into account all phenomena; rather, they select those phenomena they can deal with.”

2. “science predicts predictable phenomena”

3. “Despite these failings of our explanation for the structure, we believe it is the best candidate for being the solution.”

4. “in the middle of the 19th century, physicists started using complex numbers to discuss waves. In the 20th century, complex numbers became fundamental for the study of quantum mechanics.”

5. “the octonions as fundamental and all the other number systems as just special subsets of octonions. The only number system that really exists is the octonions. To paraphrase Leopold Kronecker, "God made the octonions, all else is the work of man." The octonions contain every number that we will ever need”

6. “This is similar to what we are doing in physics. We do not look at all phenomena. Rather, we pick out those phenomena that satisfy the requirements of symmetry and predictability. In mathematics, we describe the subset with the axiom that describes it. In physics, we describe the selected subset of phenomena with a law of nature.”

7. “As physics progresses and we become aware of more and more physical phenomena, larger and larger classes of mathematical structures are needed and we get them by looking at fewer and fewer axioms.”

8. With the final concluding sentence… “Rather than looking at the universe, we should look at the way we look at the universe.”

Are really excellent.

It leads to a question, while describing some portions of Universe, if some mathematical structure is used, later we find some undefined area or singularities…. We will be left with no alternative except to find those singularities, is it not? Or can we change the structure of mathematics to find a better solution…

Here in Dynamic universe model an attempt was made to find a singularity free tensor mathematics, which provides a solution to many of the present day Physics problems.

Many papers and books were published by the author on unsolved problems of present day Physics, for example ‘Absolute Rest frame of reference is not necessary’ (1994) , ‘Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe’, About “SITA” simulations, ‘Missing mass in Galaxy is NOT required’, “New mathematics tensors without Differential and Integral equations”, “Information, Reality and Relics of Cosmic Microwave Background”, “Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.”, in 2015 ‘Explaining Formation of Astronomical Jets Using Dynamic Universe Model, ‘Explaining Pioneer anomaly’, ‘Explaining Near luminal velocities in Astronomical jets’, ‘Observation of super luminal neutrinos’, ‘Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up’, “Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto” etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

With axioms like… No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

Dynamic Universe Model gave many results otherwise difficult to explain

Have a look at my essay on Dynamic Universe Model and I request your esteemed opinion…

Best wishes…………….

=snp. gupta

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Dear Professor Noson Yanofsky

You essay is very interesting. You clearly see the problem in modern physics. I also think on the problem “where is the boundary between science and non-science?” If we consider that it is the metaphysics shape public opinion through the media it is a real danger that an adequate conception of science, its methods and ways of existence in the public mind...

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Dear Professor Noson Yanofsky

You essay is very interesting. You clearly see the problem in modern physics. I also think on the problem “where is the boundary between science and non-science?” If we consider that it is the metaphysics shape public opinion through the media it is a real danger that an adequate conception of science, its methods and ways of existence in the public mind will be replaced by substitute of abnormal knowledge.

Today humanity is in deep crisis associated with the transition to a new techno-economic paradigm - the knowledge economy. It uses the knowledge to generate tangible and intangible values. This requires abandoning the biblical paradigm based on myths. This paradigm has lost its relevance for the management of large masses of people, as it is based on mythology and distortion of objective knowledge. For example, the relativistic world view does not contradict the Old Testament in which God created the world not from the finished material but created the matter itself. Therefore, all the experimental data that contradict the relativistic worldview are falsified or silenced. Today, the struggle for resources in the modern world of physics is reduced to competition of hypotheses and as a consequence to fight without rules on the basis of clericalism and postpositivism.

I am in more agreement with you, that the job of physics is to describe a function from the collection of observed physical phenomena to mathematical structure. The basis of any science is the experiment that is why the science was called natural philosophy. In mathematics the experiments are not used. It is based on axioms and theorems. So formally it should not be considered as science. Of course, the mathematics is very important for science as well as it allows you to see patterns and to predict new effects, i.e. it is a kind of glasses to the experimenter. So the question is – Are the glasses we choose proper?

So the "elegant" mathematical equations, which are attributed to some physical phenomena, often do not allow us to see the fallacy of the original physical models that are used in mathematical physics, and are essentially metaphysical.

More detailed information on the subject can be found in Galactic Internet and Femtotechnologies

Femtotechnologies Presentation

Quantum_Astronomy_Part_II

My best wishes

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Dear Noson,

i now read your essay in detail. It is written in clear language, simple to understand and the lines of reasoning can be traced very easily. Good work.

You contrast order with disorder, structure with chaos. You seem to have a rather pessimistic view on things like goals and intentions. But nonetheless, you argue your case very well and stringently. Let me annotate some...

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Dear Noson,

i now read your essay in detail. It is written in clear language, simple to understand and the lines of reasoning can be traced very easily. Good work.

You contrast order with disorder, structure with chaos. You seem to have a rather pessimistic view on things like goals and intentions. But nonetheless, you argue your case very well and stringently. Let me annotate some thoughts i had during the reading.

Firstly, if considering the contest’s questions, i think one has to presuppose as an axiom that all that exists does all things the right way. If we drop that assumption, we end up at nihilism. So i presuppose that the universe and its possible causes and all the rest is a consistent whole.

Your take on mathematical number systems is fascinating, innovative and thought provoking to me. The progression in the dimensionalities of the mentioned number systems is clearly an expression of logic, it is a kind of algorithm and it has therefore structure. In contrast to this – as you annotated at the end of your essay – one may arrive with such a progression at a level of description of ‘all there is’ which seems to say that the universe, viewed objectively, is devoid of structure. The interesting question is (and i formulated similar questions at the essay page of Cristinel Stoica) how order and disorder, randomness and information are intertwined.

If the mentioned progression of the dimensionalities of number systems indeed leads to the conclusion that the universe is devoid of structure, this would pose serious questions. For example, does it make sense right from the start to extrapolate a mathematical algorithm like the one for building up ever higher dimensional number systems? Isn’t this somewhat similar to Cantors cardinalities, building up ever higher infinities out of a simple algorithm? Surely, your progression should not be infinite but terminate at a certain level where no axioms are left. Although i am not a mathematician and certainly not an expert on octonions and so forth, i ask myself how can such a progression of number systems be able to drop one axiom after the other, until there are no axioms left? But taking it as given, what you arrive at is simply a tautology, namely a ‘number system’ (although without any axioms) saying that the universe and all the rest is just what it is (without specifying it further). Obviously this is plainly true, indeed the universe and all the rest is just what it is. One does not need a single axiom to conclude this!

The problem only arises when one wants to specify the whole thing due to a certain category. I assume it to be true that our universe has many phenomena which do not have goals and intentions. But this does neither imply that the universe’s main characteristic must be termed as ‘chaos’, nor does it mean that the universe’s existence and the many ‘mindless’ phenomena in it are senseless from a higher point of view. Maybe mindless phenomena serve a higher purpose; surely, this purpose then had to be determined via the construction and rules of the universe and also surely not by some physical mechanisms, but by an entity which has goals and intentions. I see no contradiction that randomness, chaos and disorder cannot support goals and intentions. This may be a hard to swallow statement, but i will explain it further.

As you know, a perfectly random sequence of 0’s and 1’s follows a certain mathematical law. The digits 0 and 1 should be evenly distributed over the whole pattern. Random in this case means that the occurrence of either of the two digits does not depend on the value of the preceding or following values of such digits. Every event should be totally independent of each other event. Have we catched ‘chaos’ and ‘randomness’ with this? In no way. We only catched the extreme case at one end of the continuum of order. ‘Randomness’ as a nihilistic ontological fact should have other features, i suspect. It should be not catched up with any mathematical description. For example, imagine that you are a kind of Boltzmann brain, but without all the physics needed for it. Just imagine you are aware of something. This something does not reveal any correlations. At one time you see a flash, then you see the flasch forming to a vague kind of bubbeling-up of some melted cheese-like thing, you see all sorts of visual impressions and they do not make any sense to you. ‘Randomness’ defined as this would be just like a nightmare.

Now, let us elevate the mathematical concept of randomness to perhaps meet what you intended to say in your essay’s last paragraphs. Maybe the observed structure of our universe is a lucky fluke within a chain of random events (like the 0’s and 1’s, randomly encoding some kind of theory of everything). Would this be a convincing scenario to explain the order in our universe and its – assumed – dichotomy to the observed chaos in our universe? I would say no, because it does not answer where the randomness comes from, how and on what existencial features it operates on and why it can be mathematically explored to the point where it produces conscious beings which indeed then mathematically have explored it.

The whole point for me here is to say that behind the concepts of randomness and order, there must be a common fundamental origin of all of this. Alternatively one must conclude that reality is somewhat irrational. Because i am not the kind of Boltzmann brain described above, i conlude that behind the interplay between randomness and order, there is some deeper origin of all there is. As you envisioned with the progressions of number systems, mathematics seems to be able to transcend itself – in the sense that its very limits show us how the universe cannot be. It cannot be infinitely dividable, it cannot be overall deterministic and at the same time be overall consistent, it cannot be overall chaotic and nihilistic in a Boltzmann-brain sense and it cannot capture the whole of existence. All this cries out for an explanation that is metaphysical. It is no wonder that the progression of number systems tends to converge towards a non-axiomatic description of reality. Because mathematics cannot capture all there is due to the nature of it. Its nature is not overall compressible. But this does not mean that for explaining the nature of reality otherwise than with mathematics, one wouldn’t need some axioms. My axioms are that there are realms beyond space and time from which our universe originated. It is limited in time, duration and space. At the outer borders (at the microscale) of this universe, quantum mechanics rules and spontaneous collapses occur. These collapses may not have an explanation in terms of physical causality, but i am convinced they have an explanation in terms of purpose and intention. For me, it is no problem to think of a creator that has the power to give some order to his creations to behave spontaneously (although here again, this spontanity is restricted by the rules of QM, also given by this creator). Surely, these considerations are all axioms, choosen by me, they do not arise necessarily from what i have written. But i see no alternatives between a creator and nihilism, the latter in the sense that reality is absurd and logics cannot conclude something logical from the fact that logics has its limits in deducing the ultimate layer of reality. But it surely can *induce* these layers on the basis that logics has realized its own deductive limits. Therefore i tend to say that logics, as an expression of a formal system, is as incomplete in the sense of Gödel’s results as every other formal system subject to Gödels results. The main result for me is that the limits of deducability do not necessarily mean that the universe is absurd. It is open for the possibility being not so. This openness is installed even within the very structure of logics, since logics can discriminate between a possibility and a necessity.

I would be happy if you could write what you think about this all.

Best wishes

Stefan Weckbach

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Dear Noson,

I can’t agree with your argument quite as you put it, but I think you’re on the right track. I like the premise “that the universe is chaotic and lacks structure,” and that something “acts like a sieve” to pull out only the very small subset of phenomena we actually observe. But as you note, it hardly seems reasonable to make scientists the primary agency of the...

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Dear Noson,

I can’t agree with your argument quite as you put it, but I think you’re on the right track. I like the premise “that the universe is chaotic and lacks structure,” and that something “acts like a sieve” to pull out only the very small subset of phenomena we actually observe. But as you note, it hardly seems reasonable to make scientists the primary agency of the selection process. I would rather say that science involves the discovery of nature’s own selection rules, which are complex and operate on many levels.

You say at the start – “These laws of nature are fine-tuned to bring about life, and in particular, intelligent life.” Well, they are evidently fine-tuned, and they do support life, but I argue in my essay that the structure of the physical world makes the emergence of life exceeding difficult. And while biological evolution did eventually produce quite intelligent animals, the leap to our human kind of intelligence hardly looks to be preordained in the selective principles of biology, much less in the laws of physics. This entire history looks much more like a series of unlikely accidents than something built into the structure of the universe from the start.

My suggestion is that physics itself provides the “sieve” – specifically, in the complex system of recursive processes that scientists make use of when they observe and measure things. We humans aren’t responsible for the fact that physics has a complicated set of symmetries that can make all its components empirically observable. Nor is this something the universe does just for the sake of intelligent observers.

I argue that in order for any kind of information to be meaningfully definable or communicable, there always needs to be a context consisting of other definable and communicable information. The physical world clearly provides such contexts… that is, the observable universe consists of the subset of structureless chaos that not only has structure, but succeeds in defining all its own structure and communicating it interactively. This is the source of the predictability of phenomena, and the many kinds of symmetry that make it work – which we observers take advantage of for our own ends.

In any case, I appreciate your imaginative line of thought here and the clarity of your writing.

Thanks – Conrad

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Dear Noson Yanofsky,

I enjoyed your essay, and found fascinating the idea of thinking of octonions as fundamental and all other number systems as subsets of the octonions. I very much like your statement: "All the axioms that one wants satisfied are found "sitting inside" the octonions."

You rightly focus on symmetry in physics. While much of particle physics is based on...

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Dear Noson Yanofsky,

I enjoyed your essay, and found fascinating the idea of thinking of octonions as fundamental and all other number systems as subsets of the octonions. I very much like your statement: "All the axioms that one wants satisfied are found "sitting inside" the octonions."

You rightly focus on symmetry in physics. While much of particle physics is based on symmetry [such as SU(3)xSU(2)xU(1)] these are not 'exact' symmetries in that the masses of the particles are not equal. In fact, approximate symmetries are applied to cases where one mass is almost 100 times greater than another. Yet these approximate symmetries still yield results.

I believe your key point is that physicists act like a sieve and significantly constrain the class of problems they tackle, limiting themselves for the most part to predictable regularities. At the end of your first paragraph you ask "What exactly are these laws of nature and how do we find them?"

In my reference 5 (The Automatic Theory of Physics) I design a robot physicist to derive theories (models) of physics from observational data. The general approach, group the numbers via inter-set and intra-set distances to derive feature vectors, is summarized in my endnotes. Thirty years later Schmidt and Lipson applied this theory via pattern recognition algorithms to

"automatically search motion tracking data captured from various physical systems…"

Whereas I had treated little more complicated than trajectories of rocks, etc, Schmidt and Lipson treated complex systems such as weights on springs and the double pendulum. In other words, systems with predictable regularity as you note. Based on their pattern recognizing robot they found:

"Without any prior knowledge about physics, kinematics, or geometry, [the robot] discovered Hamiltonian's, Lagrangians, and other laws of geometric and momentum conservation."

This agreed with my theory. However what I found most fascinating was that they found the 'type' of law that the robot derived was determined by what variables were presented to the robot observer. They discovered:

"… if we only provide position coordinates, the algorithm is forced to converge on a manifold equation of the system's state space. If we provide velocities, the algorithm is biased to find energy laws. If we additionally supply accelerations the algorithm is biased to find force identities and equations of motion."

Especially with regard to your question, 'how do we find these laws' I hope you find this as interesting as I do.

My very best regards,

Edwin Eugene Klingman

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